Flight simulator motion systems, or in short flight simulators, are provided with 6 degrees of freedom motion systems. Flight simulators provide motion cueing fidelity from manoeuvres through filtering of angular accelerations and (linear) specific forces. These signals are important for pilot perception, and therefore the motions of the flight simulators should be brought into agreement with motions of an actual aircraft. The following algorithms are found in prior art methods for controlling flight simulators.
Centroid Transformation
As it is the intention to simulate motion as perceived by the pilot, the flight simulator is located hypothetically in the aircraft with corresponding pilots' reference point P (FIG. 4).
The following logic (FIG. 8) is always encountered in literature (see Russell V. Parrish, James E. Dieudonne and Dennis J. Martin Jr., “Motion software for a synergistic six-degrees-of-freedom motion base” p. 9, NASA TN D-7350, December 1973/M. Baarspul, Delft University of Technology, “The generation of motion cues on a six-degrees-of-freedom motion system” p. 5, Report LR-248, June 1977/G. A. J. van de Moesdijk, F. L. Van Biervliet, Delft University of Technology, “Investigation to improve the motion software of the Fokker F-28 flight simulator” p. 4, Report LR-358, September 1982) and in practical applications:
Specific forces are computed in the aircraft at the hypothetical platform centroid location according to the formulas given in: O. H. Gerlach, Technische Hogeschool Delft, “Vliegeigenschappen 1” p. 227, Dictaat D 26, October-November 1981/M. Baarspul, Delft University of Technology, “The generation of motion cues on a six-degrees-of-freedom motion system” p. 6, Report LR-248, June 1977:
For example in the y-direction:Aycentroid=Aycg+(pq+{dot over (r)})·xcac+(rq−{dot over (p)})·zcac with Ay-centroid the y-component of the specific force at the hypothetical centroid location of the simulator with respect to the aircraft reference system, Ay-cg the y-component of the specific force at the centre of gravity of the aircraft, p the roll rate, q the pitch rate, r the yaw rate, {dot over (p)} the roll angular acceleration, {dot over (r)} the yaw angular acceleration, xc-ac the x-coordinate of the centroid in the aircraft reference system and zc-ac the z-coordinate of the centroid in the aircraft reference system. In most cases zc-ac is being neglected.
The motion program uses the 3 corrected specific force components Ax-centroid, Ay-centroid, Az-centroid and the 3 angular rates (or accelerations) p, q, r as input. The 6 output signals of the motion program command the motion platform centroid position (3 co-ordinates) as well as the 3 Euler angles.
Roll Angular Acceleration Simulation (FIG. 9)
Roll rate multiplied with a down tuning gain Kd is filtered through a roll high pass filter (1st or 2nd order). The co-ordinating path uses lateral sway in order to keep “gravity alignment”. In order to keep lateral position within the simulator boundaries, lateral position is sent through a y-wash-out filter, generally 2nd order. The output of the program is simulator roll angle φ and centroid position y.
These filters may be adaptive which means that Kd could be continuously adapted according to a given cost criterion.
Lateral Specific Force Simulation (FIG. 10):
Lateral specific force computed at the hypothetical centroid position is multiplied by a down tuning gain and is then sent through two different filters: a high pass position filter and a low pass angular filter. These filters are in most cases of 2nd order and are not complementary. They may well be adaptive. Again the output of the filters is ‘centroid position’ and not the position of the pilot.
Prior art flight simulators, with at least sway and roll as a degree of freedom, invariantly behave as follows: when considering flying co-ordinated turn only by means of aileron input, at the beginning of the maneuver, pilot's perception seems to be correct. The roll onset as well as lateral specific force onset are perceived. A few moments later however, one notices a spurious opposite lateral specific force. It feels like if the aircraft were in a sideslip, which is not the case.
Also during ground-taxi manoeuvres, there is very little correlation between lateral motion perception and visual information. One always has the impression of side slipping on the runway.
These problems are set out in more detail below.
Roll Manoeuvre
Consider a typical flight simulator motion response in FIG. 11 to the step aileron input maneuver of FIG. 6.
For the graphs, 2nd order filters were used as they are most often being used. The only input to the filters comes from roll rate. There is no input to the lateral specific force filter as z-position of the centroid (zc-ac) is in most cases neglected.
Angular roll acceleration (FIG. 11.4) shows a sign reversal which is inherent to high pass filtered roll acceleration.
The time response of the lateral specific force at the pilots' reference point P (FIG. 11.5) shows the following characteristics:
1° Initial peak value is correct. This acceleration is due to Δ*{umlaut over (φ)}. The centroid transformation as previously discussed only takes into account the hypothetical position xc-ac of the centroid relative to the aircraft centre of gravity (c.g.). There is no consideration for the vertical co-ordinate zc-ac of the centroid nor with the distance Δ, the vertical distance between the pilot's reference point P and the centroid c, i.e. the geometrical centre of gravity of the simulator platform. As the pilot is situated in the aircraft above the point of initial roll acceleration and as the simulator is driven to roll around its centroid, the initial lateral specific forces are roughly similar in the aircraft (a/c) and in the simulator (sim).
2° This initial peak is followed a few moments later by an important opposite spurious side force. This spurious force is detrimental to the flight simulator motion fidelity. It can be found in literature as “leaning, student on the pedals, not in phase” etc. (J. B. Sinacori, Northrop Corporation, “A practical approach to motion simulation” p 13, AIAA paper 73-931, September 1973/Susan A. Riedel and L. G. Hofmann, Systems Technology Inc., “Investigation of nonlinear motion simulator washout schemes” p 524, p 530, Proceedings of the 14th Annual Conference on Manual Control, November 1978/Susan A. Riedel and L. G. Hofmann, STI, “Manned engineering flight simulator validation” p. 172, STI-TR-1110-1, AFFDL-TR-78-192-FT-1, February 1979/David L. Quam, University of Dayton, Ohio, “Human pilot perception experiments” p. 263, Proceedings of the 15th Annual Conference on Manual Control, November 1979/Irving L. Ashkenas, STI, “Collected flight and simulation comparisons and considerations” p. 16-26, AGARD CP408 Flight Simulation, October 1985).
This phenomenon is entirely due to the presence of the y-washout filter as illustrated in FIG. 9. If there weren't such a filter, platform movement would remain perfectly co-ordinated. However the simulator would wander away. The y-washout filter is necessary to “call back” the simulator, hence introducing “un” co-ordination.
The only way to suppress this phenomenon in the existing scheme is to reduce the gain Kd to very low values. One doesn't perceive any movement any more through motion, however this is considered less worse than spurious motion.
Ground Taxi Manoeuvre
During taxi manoeuvres on ground the simulated aircraft does not roll, so only the lateral specific force filters play a major role.
There is always distortion in perceived motion: when using the rudder or nose wheel steering, initial response is felt (from the y hp filter). When this fades away sustained lateral acceleration comes up from the φ low-pass filter. Both movements do not blend into each perfectly as the filters are not complementary.